{
  "abstract": "We study mixed symplectic sums along connected unbranched cyclic multisections of degrees $p,q\\geq 2$ in ruled surfaces. With \\[ p(g-1)=q(h-1)=n, \\] the resulting four-manifold has signature zero and Euler characteristic \\[ e=4n\\left(1-\\frac1p-\\frac1q\\right). \\] We classify the types having the rational cohomology ring of $\\#_k(S^2\\times S^2)$. They occur only for odd $k$ and, with $t=(k+1)/2$, $a=g-1$, and $b=h-1$, are exactly the solutions of \\[ n=a+b+t,\\qquad a\\mid b+t,\\qquad b\\mid a+t. \\] For each odd $k$ there are finitely many types; we give an explicit parametrization and tables for $k\\leq 15$. Every type admits an equatorially product-framed symplectic realization and, possibly with different framings, a spin realization whose free integral intersection form is $kH$. We prove minimality, boundary incompressibility, an integral Mayer--Vietoris presentation, and a regular cyclic cover of degree $\\operatorname{lcm}(p,q)$. The boundary subgroup $π_1(Σ_G)\\times\\mathbb Z$ embeds in the fundamental group; this gives a nontrivial Bass--Serre splitting and rules out word-hyperbolicity, cocompact real- or complex-hyperbolic lattices, and torsion-free cocompact irreducible bidisk lattices. There are five types for $k=3$ and seven for $k=5$; for $k=1$ we recover the degree pairs $(2,3)$, $(2,4)$, and $(3,3)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03756",
  "author_total": 2,
  "authors": [
    {
      "name": "Anar Akhmedov"
    },
    {
      "name": "Azer Akhmedov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bs7mbhht4z969.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03756",
  "fulltext_url": null,
  "id": "bs7mbhht4z969",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03756",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7220707173",
  "pdf_url": "https://arxiv.org/pdf/2610.03756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bs7mbhht4z969.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.03756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher Braided Mixed Sums, Intersection Lattices, and Symplectic Four-Manifolds",
  "title_text": "Higher Braided Mixed Sums, Intersection Lattices, and Symplectic Four-Manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/bs7mbhht4z969",
  "venue": "arXiv",
  "versions": []
}